The hot topic in basketball these days is the measurement of a basketball player’s productivity. For years we have had the traditional box score which can be viewed through the lens of NBA Efficiency, TENDEX, Points Created, PERs, Game Score, Wins Shares, Win Score, and Wins Produced. And then we have the non-box score approaches of plus-minus and adjusted plus-minus. With all these measures out there, it seems unlikely that we need to call attention to anything else. Nevertheless, I thought I would devote a post to a measure that’s in my morning paper each day.
The Miller Metric
Each morning the Salt Lake Tribune is delivered to my house in Cedar City. Not surprisingly, the Utah Jazz gets quite a bit of coverage from this paper. And part of this coverage is a measure of performance that I don’t think is seen much outside of Utah. Larry Miller – the long-time owner of the Jazz who recently passed away – devised a measure called the Miller Metric. The measure is calculated as follows:
Miller Metric = Points + Rebounds + Steals + Blocked Shots + Assists – Turnovers – Shot Attempts – Personal Fouls
Each time the Jazz play the Miller Metric is reported and it’s also part of the season statistics reported for the team.
Looking at the Miller Metric I am reminded of Win Score, or the simple measure of performance we introduced in the Wages of Wins.
Win Score = PTS + REB + STL + ½*BLK + ½*AST
– FGA – ½*FTA – TO – ½*PF
These two measures are not exactly the same. The obvious differences included the weighting of blocked shots, assists, and personal fouls, as well as the inclusion of free attempts in Win Score. But the measures are similar in how shooting efficiency is treated. Unlike NBA Efficiency, TENDEX, Points Created, PERS, and Game Score; Win Score and the Miller Metric require players to shoot efficiently from the field. Specifically, instead of subtracting missed shots (the approach taken by NBA Efficiency), bothe the Miller Metric and Win Score subtract field goal attempts. Consequently, despite the differences cited, the Miller Metric (per 48 minute) and Win Score (per 48 minute) have a 0.92 correlation (from 1977-78 to 2007-08).
Evaluating the Jazz
To see the similarities, Table One presents evaluations of the Utah Jazz – after 60 games – by both metrics.
Table One: Evaluating the Utah Jazz in 2008-09 with PAMM and PAWS
Table One presents position adjusted figures for both measures. For the Miller Metric the position adjusted measure – what I call PAMM [Position Adjusted Miller Metric] – is not as necessary. This is because free throw attempts are ignored by the Miller Metric (at least, I get the numbers the Tribune gets when I ignore free throw attempts). As a consequence, although shooting efficiency from the field is required by the Miller Metric, from the line efficiency is not required (i.e. the more you shoot from the line the better you will look regardless of free throw percentage).
If you add free throw attempts to the Miller Metric – by subtracting ½*FTA from this measure – the correlation with per 48 minute Win Score rises to 0.94. And then a position adjustment will clearly be required. In other words, as you move from a measure that focuses more on scoring totals to one that focuses more on scoring efficiency, you have to consider where a player is playing on the court.
Regardless of the free throw attempt issue, there are clear similarities between both PAMM and PAWS (Position Adjusted Win Score). The top six players on the Jazz – Carlos Boozer, Deron Williams, Andrei Kirilenko, Paul Millsap, Ronnie Brewer, and Mehmet Okur — are the same by both measures. And both measures regard these six as the only above average players on the team. In sum, both PAMM and PAWS are telling similar stories.
If we turn to WP48 [Wins Produced per 48 minutes] – as reported in Table Two – we again see the same story. The Utah Jazz again have six above average players and three players – Ronie Price, Morris Almond, and Jarron Collins — who rank as the least productive players on the team.
Table Two: Evaluating the Utah Jazz after 60 games in 2008-09 with Wins Produced
In sum, it appears that Larry Miller was on to something. By creating a measure that emphasized shooting efficiency from the field he created a metric that comes fairly close to a player’s contribution to wins.
Finding Talent in Utah
Of course it’s not clear how much this measure informs decision-making in Utah. After all, most owners are not picking players on their teams. Nevertheless, I think one can make an argument that Utah does have some ability to find productive players.
To see this, consider the trajectories of the two teams that met in the NBA Finals in 1997-98. After the 1998 Finals the Chicago Bulls saw a number of players responsible for their title depart. The duo of Stockton and Malone – the two players who led the Jazz — stayed together for five more seasons. And across these years the Jazz managed to keep making the playoffs.
Given these scenarios, one would think Chicago would have re-built faster. While Utah kept appearing in the post-season, Chicago kept adding top-10 picks in the draft (see Elton Brand, Marcus Fizer, Jamal Crawford, Eddy Curry, Jay Williams, Kirk Hinrich, Ben Gordon, Tyrus Thomas, Joakim Noah, and Derrick Rose). But despite these additions, Chicago – across the past 10 years – has yet to win 50 games in the regular season. Meanwhile Utah – if it can win 13 of its last 22 games this year – will have reached the 50 win threshold for the third consecutive season.
Again, we don’t know the Mille Metric has been used to select players in Utah. But of the six above average players on the roster, only one (Deron Williams), was a top ten choice in the draft. So apparently the Jazz – despite lacking the advantages in the draft bestowed on the Bulls — have some ability to find productive players. And it’s just possible the Miller Metric – with its emphasis on shooting efficiency (at least from the field) – has helped.
Then again, maybe this is just something that makes my morning paper in Utah a bit more interesting.
– DJ
The WoW Journal Comments Policy
Our research on the NBA was summarized HERE.
The Technical Notes at wagesofwins.com provides substantially more information on the published research behind Wins Produced and Win Score
Wins Produced, Win Score, and PAWSmin are also discussed in the following posts:
Simple Models of Player Performance
What Wins Produced Says and What It Does Not Say
Introducing PAWSmin — and a Defense of Box Score Statistics
Finally, A Guide to Evaluating Models contains useful hints on how to interpret and evaluate statistical models.
Wages of Wins Journal 
Dave
March 4, 2009
Larry was known to have a photographic memory and was good at math so he likely is the one who made the Miller metric and he took a far more hands on approach to the Jazz then most owners do.
Peter
March 4, 2009
Just for chagrins (and because WP48’s for these players have likely been calculated), here are Miller Metric Scores per 48 minutes for a number of All-Stars/potential MVP candidates in the league:
Kobe Bryant (SG): 21.2-9.5=11.7
Tim Duncan (C): 27.0-13.7=13.3
Devin Harris (PG): 20.5-11.6=8.9
Dwight Howard (C): 32.3-13.7=18.6
LeBron James (PF): 29.0-12.9=16.1*
Chris Paul (PG): 28.6-11.6=17.0
Dwyane Wade (SG): 25.2-9.5=15.7
*18.5 if evaluated as SF
Some quick observations:
1. As in Win Scores, Kobe Bryant is not the most productive player in the group. In fact, he is still a ways away before becoming the top performer.
2. Some rising stars like Harris, Danny Granger (8.5), and Kevin Durant (7.9) still have a ways to go before being mentioning in the same class of top-5 guys like LeBron. However, they are entering into the prime of their careers.
3. Dwight Howard is arguably the biggest beneficiary of the discarded free throw shooting numbers in the Miller Metric. Even after adjusting for position, and even if LeBron James is considered a small forward, Howard is still the most productive player in the bunch using PAMM.
4. Even approaching 33 years of age, Tim Duncan is still performing on a high level. While not as productive as say, Howard, he is still more productive than Bryant and a number of younger stars.
Peter
March 4, 2009
Addendum: LeBron’s PAMM is 18.3, not 18.5, as a SF.
dberri
March 4, 2009
Peter,
Did you include personal fouls in your calculation of the Miller Metric? I forgot to note these in the original post. And what are you using for the position adjustments in calculating PAMM?
Italian Stallion
March 4, 2009
dberri,
I like winscore a lot, but I have a question.
Have you ever considered the possibility that the contribution of each area of performance towards wins is not linear?
Let me put it another way.
Is is possible that rebounds 1 through 3 are worth less than rebounds 4-6, are worth less than rebounds 7-9, etc….. ?
The same for assists, blocked shots etc…
I’ve expressed this in the past, but I think a certain level of contribution is more or less easily replaced either off the bench or by the other players on the court.
IMO, it’s the guys that really excel in a single or multiple categories that contribute things that are tough to replace. I think they may contribute more to winning than guys that do a little of everything fairly well and earn similar win scores, NBA efficiency, Miller Metric etc.. .
Thoughts?
Italian Stallion
March 4, 2009
Another way of thinking about it might be this.
Anything you do up to the point of being average is not worth a whole lot, but everything you do that’s above average is worth a real lot.
Peter
March 4, 2009
Dave:
I had gone off of what you had originally published in the Miller Metric.
And since you had covered every position when you analyzed the Jazz, I simply subtracted the PAMM from the raw score obtained in the Miller Metric to get these averages:
PG: 11.6 per 48
SG: 9.5
SF: 10.7
PF: 12.9
C: 13.3
After all, you had to have specific numbers/positions in mind if you even calculated PAMM’s in the first place.
Here are the new scores with the updated Miller Metric.
Kobe Bryant (SG): 8.8
Tim Duncan (C): 10.3
Devin Harris (PG): 5.7
Dwight Howard (C): 14.5
LeBron James (PF): 13.6
Chris Paul (PG): 13.5
Dwyane Wade (SG): 12.8
Howard remains the most productive player in the group, although James, who has played multiple positions, is the most compelling challenger.
And even after all the adjustments, Bryant, at least on the floor, is not the “best” player in the game.
axim
March 4, 2009
Dberri, recently there has been a lot of discussion about the use of advanced statistics in basketball and what they really mean. Most people who have come up with their own formula believe that advanced metrics are great, but they can only tell so much. Meaning that while they certainly help understand who is a productive player, the rankings that these metrics produce are not exact and should only be used as a tool to help, not the be-all end-all.
So my question to you is do you believe that by looking at Wins Produced you truly have a metric that ranks players exactly where they should and describes all their production, or do you just find it a useful tool that gives you a much better understanding of the game and players?
dberri
March 4, 2009
axim,
Quick answer…
When it comes to plus-minus and adjusted plus-minus what you say is true. The standard errors on the estimates are so large that for most players the coefficients are statistically insignificant (by conventional standards). So it is not clear what these coefficients mean.
As for the box score methods… as noted these typically overvalue scoring totals (or undervalue shooting efficiency). When you correct that problem, you find that the box score does tell you quite a bit about the productivity of a player.
In sum, I don’t think it is the case that the box score can’t tell you who is productive (and who is not). The key is looking past the column in the box score that lists how many points a player scored. There is more to the game than scoring totals.
stephanie
March 4, 2009
Should the rest of the league be concerned that the Spurs now wield the power of Gooden’s beard?
axim
March 4, 2009
I understand this. Obviously you are a believer in Wins Produced, and with good reason. But my question is say a player has a WP of .278 and another has a WP of .255, do you automatically believe the player with a WP .278 is a more productive player, or do you think their Wins Produced say these players are both very good players and it is too close to tell, and other factors (maybe such as non box-score intangibles) should be accounted for?
dberri
March 4, 2009
axim,
I don’t like the word “believer.” This is not a religion. I like to think we are doing science. So I tend to think Wins Produced paints a fairly accurate picture because the evidence points in that direction.
That being said, two players with the numbers you report are essentially the same. 0.26 and 0.28 yields about the same outcomes.
As for non-box score factors… there are factors that cause performance of a player to change that can be quantified. In forecasting performance, these other factors (coaching, productivity of teammates, age, etc….) need to be considered.
rincewind
March 4, 2009
I’m confused as to why you keep evaluating Lebron as a PF, Peter.
He doesn’t really play PF very much.
mrparker
March 5, 2009
82games.com has him playing 21 percent of the teams minutes at PF. He has played 55 percent of the teams minutes at sf according to them. So, that means he’s played about 27 percent of his own minutes at power forward. When he’s playing pf his fg,fta, reb, and blocks per 48 minutes all increase while his fouls and to increase as well.
Italian Stallion
March 5, 2009
I totally disagree with the idea that a SF that plays some PF should be penalized because some of his stats don’t compare favorably to other PFs.
If anything, the ability of some SFs to play PF competently is something that makes him more valuable and a BETTER PLYER!
What coach wouldn’t perfer that his players be versatile enough to take advantage of certain matchups, give rest to key players when required, fill in better during injures etc…
To me, James is a SF that should get extra credit because he CAN play PF well also. Same with Larry Bird. A guy like Magic Johnson had versatility that was incredibly valuable. That was proved when he actually played some C.
Do you really want to rate Magic lower because he could play every position?
Italian Stallion
March 5, 2009
dberri,
I was really hoping you would address my question?
Win Score = PTS + REB + STL + ½*BLK + ½*AST – FGA – ½*FTA – TO – ½*PF
Let say player A = 15 + 5 + 1 + .5 + 2.5 – 12 – 3 – 1 -1.5 = 6.5
Let’s say player B = 13 + 4 +1 0 + 6.5 – 13 – 3 – .5 – 1.5 = 6.5
Both players have the same WinScore.
Player A does a little of everything, but nothing especially well.
Player B is not as quite as good as A at most things, but he’s obviously a GREAT passer.
Is is possible that being great at one or more things but so so at the rest is better than being average or so at everything?
It seems to me that players like A are a dime a dozen, but B’s unique talent could be extremely valuable if the other players compliment him well and make up for some of his deficiencies.
Peter
March 5, 2009
rincewind,
The greatest challenge in trying to put a number on LeBron is that he plays multiple positions.
I decided to evaluate him as a PF under the assumption that Mo Williams was the PG, Delonte West was the SG, and Wally Szerbiak the SF.
Actually, LeBron is probably more productive than Howard, since Ben Wallace and Big Z have played a lot of PF and C. However, it’s very tough to nail down one particular position with James.
Personally, I would name LeBron the NBA’s MOP and Howard Defensive POY.
Joe
March 5, 2009
IS,
This is a quote for Dave… “In calculating Wins Produced, we simply look at the value of the statistics in terms of wins. So Wins Produced are a measure of how productive the player has been. But it doesn’t tell us why.”
I think that a coach playing Lebron at PF would fall into the “why” factors if it negatively affected his individual contributions.
Italian Stallion
March 5, 2009
Joe,
I have no problem with that kind of interpretation, but typically people think of Wind Produced (and other measurements) in terms of measuring who the best players are.
I’ll take a PG that can play every position including C over a PG that can only play PG even if his Wins Produced is a little lower because of the positional adjustments.
To me, Lebron’s ability to switch to PF makes him a better player. IMO, he is probably producing MORE wins by being able to switch to PF – assuming the coach is using him and the other assets effectively.
Ken
March 5, 2009
IS,
If LeBron playing PF helps his team, it would show up in his stats. He’s quicker than most PF’s, so he should be able to get to the basket more, upping his FG%, and shoot more free throws, increasing his win score. On the other hand, he might not get as many rebounds as a typical PF, but he might get more steals, and possibly more blocks coming from the weak side, etc. In other words, him moving to multiple positions could have subtle fluctuations in his stats, and if it is a real benefit, it will show up in the box score. As it is, his win score is ridiculously high every game…
Italian Stallion
March 5, 2009
Ken,
I understand what you are saying, but my impression has been that guys like Bird and James that play a combination of SF and PF tend to get hurt statistically by being compared to other PFs that are usually more productive than SFs.
If you are just trying to determine contribution to WINS, perhaps the team is not as good as when they play SF and another solid player is playing PF (McHale). But from my perspective, the coach must be seeing some advantage to using them at PF from time to time. So I think it’s important to view versatility as a PLUS when evaluating how good the player is.
I’m a huge Knicks fan.
IMO, Wilson Chandler is a decent long term prospect even though he has only been mediocre this year statistically. However, he has played some PF, SF and SG depending on the matchups. I think that has been valuable to the Knicks because they could mix and match other players at other spots to take advantage of other matchups and it helped when they were shorthanded.
axim
March 5, 2009
by Lebron playing PF, (and this is assuming that Coach Brown knows what he is doing), he is allowing other people to play at positions where they are more comfortable and more productive. So I think what IS is saying that Lebron may take a personal hit by playing PF, but because he is doing it he allows his other teammates to be more productive at their respective positions, instead of throwing somebody else in at power forward. So if that is the case, should Lebron be penalized?
Italian Stallion
March 5, 2009
axim,
Thanks. Expressing myself with words is not one of my strong points. LOL
Jason E
March 5, 2009
With so much of the criticism of WP summing to “you overvalue rebounds”, it’s refreshing to see some discussion of the position correction.
The issue of “penalized” makes it sound like the issue is one of some archetype of fairness. This shouldn’t be at all relevant. It’s science, and at the heart of it is whether or not the model has predictive value, whether the way it records past events makes it useful for predicting future events, and to what degree.
WP measures the statistical factors that influenced win probability and apportions them to individual players. One of the assumptions of the model is that position matters. This is an assumption, one used to correct for the fact that in general centers and PF collect more of the stats that factor into win probability than do guards, but this does not mean a team can do without guards. Indeed the anecdotal evidence is that some teams can perform reasonably well even for some extended stretches with lineups that eschew bigmen, suggesting that the value of a smaller guy, even if he doesn’t grab the stats that a center does, is significant. Is it equal (or greater? or less?) than the value of the bigman? That’s something open for investigation, but ‘fairness’ doesn’t factor into the debate when it’s about a model. The model is amoral. (I’ve heard economists be both praised and criticized for being amoral, FWIW.) The empirical results are what matters.
I do find it interesting that the summed minutes of players by listed positions are not equal. Far fewer minutes are played by players who are listed as centers (or even F/C) than for guards, suggesting that many teams do without much of the time. This may warrant a reconsideration of the assumption that position matters such that the contributions are equal or the assumption that in a game, there are as many minutes that must be filled for all positions.
But again, modification to the model shouldn’t be done in point of ‘fairness’ or because of some notion that someone is ‘penalized’, but because the model becomes more accurate as a result of the modification.
Italian Stallion
March 6, 2009
Jason,
I believe you are missing the point.
If the model was only used in the way you suggest, there would be no issue. However, people routinely use Win Porduced as a way of measuring who the best players are.
In that regard, positional adjustments are worthy of discussion. As I suggested, no one in their right mind would consider versatility a negative, but that’s exactly what happens to the perception of Lebron when he plays PF. If he refused to play PF, his stats would be better, but it would probably hurt the team.
Jason E
March 7, 2009
“people routinely use Win Porduced as a way of measuring who the best players are. ”
What do you mean by ‘best’? To whom do you reference as these “people”?